Jessica Salans, a children's book publisher, urges California residents to vote for Bernie Sanders at the phone bank at the California Nurses Association headquarters in Glendale, Calif., on June 6. She symbolizes the task Hillary Clinton faces to unify Democrats: Ms. Salans says “I know in my heart of hearts I can’t support Hillary Clinton.”

Washington — [Updated 6:10 p.m. Thursday] The Democratic Party now well and truly belongs to Hillary Clinton, but it’s not the party she thought she would inherit.

The Bernie Sanders “revolution,” fueled by Millennial fervor as well as aging ’60s-era liberals and working people feeling left behind by a changing economy, has altered what the party stands for. Free trade is out. A big increase in the federal minimum wage is in. And on foreign policy, the party may in fact stick closer to President Obama’s vision than the more interventionist approach of Mrs. Clinton.

But the precise future shape of the Democratic Party remains a work in progress, as the delicate task of wooing Senator Sanders and his followers ramps up following Mrs. Clinton’s clinching of the nomination this week. That effort took a large step forward Thursday, when Sanders met with President Obama and agreed to work with Clinton "to defeat Donald Trump and to create a government which represents all of us and not just the 1 percent."

In the final days of campaigning ahead of Tuesday’s primary, Sanders pledged to take his bid all the way to the Philadelphia convention in July. But after losing four out of six contests Tuesday, including California, Sanders headed home to Vermont to reassess.

In the end, analysts say, the Democratic Party is likely to land somewhere between the unalloyed liberalism of 1972 nominee George McGovern and the 1990s-era centrism espoused by Clinton’s husband, former President Bill Clinton. But that represents a broad spectrum.

Balancing the budget – one of Mr. Clinton’s signal accomplishments, in concert with the Republican-led Congress – surely won’t be a priority for Hillary Clinton. And while her spending priorities for social programs don’t go as far as Sanders’s, her goals are still aggressive. For example, where Sanders promises free tuition at public colleges, Clinton proposes tuition-free community college and debt-free four-year college.

Already, Clinton has distanced herself from some of her husband’s policies, such as the 1994 crime bill, which resulted in mass incarceration of African-American men. Her support as first lady for welfare reform in 1996 has been another line of attack by Sanders, who said it amounted to “scapegoating people who were helpless.” The Clinton campaign has defended the reform, saying the child poverty rate fell under President Clinton, but adds that Hillary Clinton intends to amend the program.

“For now, Sanders has pulled the party to the left, but we’ll see. Things can fade,” says Larry Sabato, director of the Center for Politics at the University of Virginia, Charlottesville.

Bernie's continuing influence

In the short run, though, Sanders will “directly influence” the platform, as well as Clinton’s choice of running mate, Professor Sabato says. “I don’t think there’s any way that Clinton can choose someone he would actively oppose,” he adds. “He will at least have to acquiesce, if not fully embrace [that person].”

But does the platform even really matter? The drafting of party platforms, on both sides, often involves intense negotiation, even if the final product is ultimately read by only the most fervent of activists, and a few diehard reporters and political scientists. In 1996, GOP nominee Bob Dole famously said that he hadn’t read the Republican platform.

“And Bob Dole didn’t get elected,” says Sabato.

Former Senator Dole lost that election for many reasons, not least, the fact that he was up against a popular incumbent in Clinton. But his indifference toward the platform spoke volumes to the party’s most devoted activists – and so in fact some connection can be drawn with his loss.

As president, Hillary Clinton would not be bound by the platform, but if she were to stray too far from it, she could face challenges keeping the base of her party happy, and in working with Democrats in Congress.

For now, Clinton faces pressure on a range of issues that have separated her from the Sanders camp. On fossil-fuel regulation, Sanders supports a nationwide ban on fracking. Clinton does not. He also supports a $15 an hour federal minimum wage, while Clinton supports $12. Though she has said she would sign legislation setting the minimum at $15. Thus the $15 minimum wage is nearly certain to wind up in the platform.

Apart from platform changes, the Sanders camp is also urging fundamental changes to the Democratic nominating system, including the existence of “superdelegates” – the unbound convention delegates who can support whomever they want, and who are backing Clinton by an overwhelming margin. Sanders decries the system as rigged and undemocratic, and his message has created momentum for the party to consider procedural reforms.

But with only the June 14 District of Columbia primary to go, the reality is that Sanders is losing the popular vote in the Democratic primaries by 3.7 million votes, and pledged delegates by 380.

Getting past bitterness

Still, his legions of supporters give him massive leverage as he contemplates his path forward. And the fact that he’s not really a Democrat – having spent his entire political career as a self-described democratic socialist – also makes him a little dangerous, in the eyes of some Democrats. Party unity may well not be his top priority.

“Clinton people are going to have to be patient, and they’re going to have to let Sanders and his campaign work their way through this,” says William Carrick, a veteran Democratic strategist based in Los Angeles. “There’s going to be a little bit of back and forth regarding the platform and probably rules.”

Mr. Carrick doesn’t sound all that concerned, though, about the party’s ability to sew together the Clinton and Sanders wings. “I’ve been in some bitter campaigns, and I don’t find this to be as bitter as sometimes the pundit class describes it.”

Carrick also sees Sanders as having done an enormous favor for Clinton: He has drawn a new generation of voters into politics and into the Democratic fold.

“Millennials are disappointed that he’s not the nominee, but then they begin to sort through it,” he says. “Instead of taking their bat and ball and going home, I think they’re going to say, ‘Better finish the job. No Donald Trump.’ ”

For now, though, Clinton has her work cut out.

Jessica Salans, a children’s book publisher in her late 20s, says she wasn’t into politics when she was younger, but has felt empowered by Sanders.

Sanders has “broken the machine,” says Ms. Salans, who lives in Los Angeles, speaking on the eve of the California primary. “Democrats used to be the party of the working people, now it’s the party of the elites and the educated middle class. That’s not the majority. Bernie’s ideas are not radical. Other countries have universal health care. Other countries have free college.”

And, she concludes, “I know in my heart of hearts I can’t support Hillary Clinton.”